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Results: Men's singles | Women's singles
Federer, the Wimbledon and Australian Open champion, was simply outclassed 6-4, 6-4, 6-4 by the Brazilian three-times former champion.
"It is a love story for me," Kuerten said. "This tournament helps me to get the best from myself."
Try as he might, Federer had no answer to the Brazilian's brilliance throughout the contest, and acknowledged the fact afterwards.
"He deserves it, he won three times here. He played really well, he deserved the crowd's support, he deserved to win," the Swiss said.
In the women's draw second seed Serena Williams eased into the fourth round with a 6-0, 6-4 victory over unseeded Croatian Silvija Talaja.
The American, champion in 2002, made 32 unforced errors but was too good for Talaja, the world number 106, winning in 67 minutes to set up a clash with Shinobu Asagoe of Japan.
Seventh seed Jennifer Capriati battled through to the fourth round with a 6-2, 3-6, 6-4 victory over Russia's Elena Bovina.
The 28-year-old American was made to fight all the way by 25th seed Bovina, one of the large crop of exciting Russian women's players on the tour.
Champion in 2001, Capriati will next meet 17th seed Francesca Schiavone of Italy.
Sixth seed Anastasia Myskina also advanced, ousting Czech Denisa Chladkova 6-3, 7-6. She will next face either Swiss Myriam Casanova or fellow Russian and 11th seed Svetlana Kuznetsova.
Kuerten was irrepressible on a scorching hot centre court, absorbing everything the world number one had to throw at him and firing winners all over the red court.
A single break in each set was all the 28th seed needed to topple the pre-tournament favourite and reach the last 16.
He will next face either Spain's Feliciano Lopez or Lee Hyung-taik of South Korea.
Federer's defeat and the loss of second seed Juan Carlos Ferrero earlier in the week leaves Argentine Guillermo Coria the highest remaining seed in the men's draw.
Women's fourth seed Venus Williams meets former champion Mary Pierce later on day six while last year's men's runner-up, Martin Verkerk, plays former world number one Lleyton Hewitt.
Results of men's singles matches (prefix number denotes seeding):
Third round
Igor Andreev (Russia) beat Julien Benneteau (France) 7-6 (7-3), 7-6 (7-3), 6-3
28-Gustavo Kuerten (Brazil) beat 1-Roger Federer (Switzerland) 6-4, 6-4, 6-4
Gaston Gaudio (Argentina) beat Thomas Enqvist (Sweden) 6-0, 6-4, 6-7 (5-7), 6-4
Results of women's singles matches (prefix number denotes seeding):
Third round
4-Venus Williams (U.S.) beat 30-Mary Pierce (France) 6-3, 6-1
23-Fabiola Zuluaga (Colombia) beat Katarina Srebotnik (Slovenia) 5-7, 6-2, 6-3
11-Svetlana Kuznetsova (Russia) beat Myriam Casanova (Switzerland) 3-6, 6-3, 6-4
2-Serena Williams (U.S.) beat Silvija Talaja (Croatia) 6-0, 6-4
Shinobu Asagoe (Japan) beat Gisela Dulko (Argentina) 7-5, 4-6, 6-4
7-Jennifer Capriati (U.S.) beat 25-Elena Bovina (Russia) 6-2, 3-6, 6-4
6-Anastasia Myskina (Russia) beat Denisa Chladkova (Czech Republic) 6-3, 7-6 (7-3)
17-Francesca Schiavone (Italy) beat Virginia Ruano Pascual (Spain) 6-2, 6-3
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